Parameter selection in permutation entropy for an electroencephalographic measure of isoflurane anesthetic drug effect

EEG entropy insights in the context of physiological aging and Alzheimer's and Parkinson's diseases: a comprehensive review

In recent decades, entropy measures have gained prominence in neuroscience due to the nonlinear behaviour exhibited by neural systems. This rationale justifies the application of methods from the theory of nonlinear dynamics to cerebral activity, aiming to detect and quantify its variability more effectively. In the context of electroencephalogram (EEG) signals, entropy analysis offers valuable insights into the complexity and irregularity of electromagnetic brain activity. By moving beyond linear analyses, entropy measures provide a deeper understanding of neural dynamics, particularly pertinent in elucidating the mechanisms underlying brain aging and various acute/chronic-progressive neurological disorders. Indeed, various pathologies can disrupt nonlinear structuring in neural activity, which may remain undetected by linear methods such as power spectral analysis. Consequently, the utilization of nonlinear tools, including entropy analysis, becomes crucial for capturing these alterations. To establish the relevance of entropy analysis and its potential to discern between physiological and pathological conditions, this review discusses its diverse applications in studying healthy brain aging and neurodegenerative diseases, including Alzheimer's disease (AD) and Parkinson's disease (PD). Various entropy parameters, such as approximate entropy (ApEn), sample entropy (SampEn), multiscale entropy (MSE), and permutation entropy (PermEn), are analysed within this context. By quantifying the complexity and irregularity of EEG signals, entropy analysis may serve as a valuable biomarker for early diagnosis, treatment monitoring, and disease management. Such insights offer clinicians crucial information for devising personalized treatment and rehabilitation plans tailored to individual patients.

Longitudinal detection of gait alterations associated with hypertension-induced cerebral microhemorrhages in mice: predictive role of stride length and stride time asymmetry and increased gait entropy

Cerebral microhemorrhages (CMHs) are of paramount importance as they not only signify underlying vascular pathology but also have profound implications for cognitive function and neurological health, serving as a critical indicator for the early detection and management of vascular cognitive impairment (VCI). This study aimed to investigate the effects of hypertension-induced CMHs on gait dynamics in a mouse model, focusing on the utility of advanced gait metrics as sensitive indicators of subclinical neurological alterations associated with CMHs. To induce CMHs, we employed a hypertensive mouse model, using a combination of Angiotensin II and L-NAME to elevate blood pressure, further supplemented with phenylephrine to mimic transient blood pressure fluctuations. Gait dynamics were analyzed using the CatWalk system, with emphasis on symmetry indices for Stride Length (SL), Stride Time (ST), and paw print area, as well as measures of gait entropy and regularity. The study spanned a 30-day experimental period, capturing day-to-day variations in gait parameters to assess the impact of CMHs. Temporary surges in gait asymmetry, detected as deviations from median gait metrics, suggested the occurrence of subclinical neurological signs associated with approximately 50% of all histologically verified CMHs. Our findings also demonstrated that increases in gait entropy correlated with periods of increased gait asymmetry, providing insights into the complexity of gait dynamics in response to CMHs. Significant correlations were found between SL and ST symmetry indices and between these indices and the paw print area symmetry index post-hypertension induction, indicating the interdependence of spatial and temporal aspects of gait affected by CMHs. Collectively, advanced gait metrics revealed sensitive, dynamic alterations in gait regulation associated with CMHs, resembling the temporal characteristics of transient ischemic attacks (TIAs). This underscores their potential as non-invasive indicators of subclinical neurological impacts. This study supports the use of detailed gait analysis as a valuable tool for detecting subtle neurological changes, with implications for the early diagnosis and monitoring of cerebral small vessel disease (CSVD) in clinical settings.

Slope Entropy Characterisation: An Asymmetric Approach to Threshold Parameters Role Analysis

Slope Entropy (SlpEn) is a novel method recently proposed in the field of time series entropy estimation. In addition to the well-known embedded dimension parameter, m, used in other methods, it applies two additional thresholds, denoted as δ and γ, to derive a symbolic representation of a data subsequence. The original paper introducing SlpEn provided some guidelines for recommended specific values of these two parameters, which have been successfully followed in subsequent studies. However, a deeper understanding of the role of these thresholds is necessary to explore the potential for further SlpEn optimisations. Some works have already addressed the role of δ, but in this paper, we extend this investigation to include the role of γ and explore the impact of using an asymmetric scheme to select threshold values. We conduct a comparative analysis between the standard SlpEn method as initially proposed and an optimised version obtained through a grid search to maximise signal classification performance based on SlpEn. The results confirm that the optimised version achieves higher time series classification accuracy, albeit at the cost of significantly increased computational complexity.

Information-Theoretic Approaches in EEG Correlates of Auditory Perceptual Awareness under Informational Masking

In informational masking paradigms, the successful segregation between the target and masker creates auditory perceptual awareness. The dynamics of the build-up of auditory perception is based on a set of interactions between bottom-up and top-down processes that generate neuronal modifications within the brain network activity. These neural changes are studied here using event-related potentials (ERPs), entropy, and integrated information, leading to several measures applied to electroencephalogram signals. The main findings show that the auditory perceptual awareness stimulated functional activation in the fronto-temporo-parietal brain network through (i) negative temporal and positive centro-parietal ERP components; (ii) an enhanced processing of multi-information in the temporal cortex; and (iii) an increase in informational content in the fronto-central cortex. These different results provide information-based experimental evidence about the functional activation of the fronto-temporo-parietal brain network during auditory perceptual awareness.

Slope Entropy Normalisation by Means of Analytical and Heuristic Reference Values

Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical [0,1] interval. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. It is based on a max-min normalisation scheme, described in two steps. First, an analytic normalisation is proposed using known but very conservative bounds. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. The results confirm the suitability of the approach proposed, using a mixture of the two methods.

Musical Emotions Recognition Using Entropy Features and Channel Optimization Based on EEG

The dynamic of music is an important factor to arouse emotional experience, but current research mainly uses short-term artificial stimulus materials, which cannot effectively awaken complex emotions and reflect their dynamic brain response. In this paper, we used three long-term stimulus materials with many dynamic emotions inside: the "Waltz No. 2" containing pleasure and excitement, the "No. 14 Couplets" containing excitement, briskness, and nervousness, and the first movement of "Symphony No. 5 in C minor" containing passion, relaxation, cheerfulness, and nervousness. Approximate entropy (ApEn) and sample entropy (SampEn) were applied to extract the non-linear features of electroencephalogram (EEG) signals under long-term dynamic stimulation, and the K-Nearest Neighbor (KNN) method was used to recognize emotions. Further, a supervised feature vector dimensionality reduction method was proposed. Firstly, the optimal channel set for each subject was obtained by using a particle swarm optimization (PSO) algorithm, and then the number of times to select each channel in the optimal channel set of all subjects was counted. If the number was greater than or equal to the threshold, it was a common channel suitable for all subjects. The recognition results based on the optimal channel set demonstrated that each accuracy of two categories of emotions based on "Waltz No. 2" and three categories of emotions based on "No. 14 Couplets" was generally above 80%, respectively, and the recognition accuracy of four categories based on the first movement of "Symphony No. 5 in C minor" was about 70%. The recognition accuracy based on the common channel set was about 10% lower than that based on the optimal channel set, but not much different from that based on the whole channel set. This result suggested that the common channel could basically reflect the universal features of the whole subjects while realizing feature dimension reduction. The common channels were mainly distributed in the frontal lobe, central region, parietal lobe, occipital lobe, and temporal lobe. The channel number distributed in the frontal lobe was greater than the ones in other regions, indicating that the frontal lobe was the main emotional response region. Brain region topographic map based on the common channel set showed that there were differences in entropy intensity between different brain regions of the same emotion and the same brain region of different emotions. The number of times to select each channel in the optimal channel set of all 30 subjects showed that the principal component channels representing five brain regions were Fp1/F3 in the frontal lobe, CP5 in the central region, Pz in the parietal lobe, O2 in the occipital lobe, and T8 in the temporal lobe, respectively.

Gait variability predicts cognitive impairment in older adults with subclinical cerebral small vessel disease

Introduction

Advanced methods of gait research, including approaches to quantify variability, and orderliness/regularity/predictability, are increasingly used to identify patients at risk for the development of cognitive impairment. Cerebral small vessel disease (CSVD) is highly prevalent in older adults and is known to contribute to the development of vascular cognitive impairment and dementia (VCID). Studies in preclinical models demonstrate that subclinical alterations precede CSVD-related cognitive impairment in gait coordination. In humans, CSVD also associates with gait abnormalities. The present study was designed to test the hypothesis that increased gait variability and gait asymmetry predict a decline in cognitive performance in older adults with CSVD.

Methods

To test this hypothesis, we compared cognitive performance and gait function in patients with CSVD (age: 69.8 ± 5.3 years; n = 11) and age- and sex-matched control participants (age: 70.7 ± 5.8 years; n = 11). Based on imaging findings, patients with CSVD were identified [presence of white matter hyperintensities plus silent brain infarcts and/or microhemorrhages on magnetic resonance imaging (MRI) assessment]. Cognitive performance was assessed using the Cambridge Neuropsychological Test Automated Battery (CANTAB). Gait parameters were measured during the single and dual tasks, during which participants, in addition to the motor task, completed a series of mental arithmetic calculations. Spatial and temporal parameters of gait variability, symmetry, and permutation entropy were determined using a pressure-sensitive gait mat during single and dual cognitive task conditions.

Results

Patients with CSVD exhibited lower performance in a visual learning test (p = 0.030) and in a sustained attention test (p = 0.007). CSVD also affected step time variability (p = 0.009) and step length variability (p = 0.017). Step lengths of CSVD participants were more asymmetric (p = 0.043) than that of controls, while the two groups were statistically similar regarding step time symmetry and entropy of step time and length. Gait variability was inversely associated with sustained attention, especially among CSVD patients, and this relationship was significantly different between the two groups. The association of sustained attention with gait symmetry was also significantly different between the two groups.

Discussion

Our findings provide additional evidence in support of the concept that increased gait variability and asymmetry may predict cognitive impairment in older adults with CSVD.

A New Framework for Automatic Detection of Patients With Mild Cognitive Impairment Using Resting-State EEG Signals

Mild cognitive impairment (MCI) can be an indicator representing the early stage of Alzheimier's disease (AD). AD, which is the most common form of dementia, is a major public health problem worldwide. Efficient detection of MCI is essential to identify the risks of AD and dementia. Currently Electroencephalography (EEG) is the most popular tool to investigate the presenence of MCI biomarkers. This study aims to develop a new framework that can use EEG data to automatically distinguish MCI patients from healthy control subjects. The proposed framework consists of noise removal (baseline drift and power line interference noises), segmentation, data compression, feature extraction, classification, and performance evaluation. This study introduces Piecewise Aggregate Approximation (PAA) for compressing massive volumes of EEG data for reliable analysis. Permutation entropy (PE) and auto-regressive (AR) model features are investigated to explore whether the changes in EEG signals can effectively distinguish MCI from healthy control subjects. Finally, three models are developed based on three modern machine learning techniques: Extreme Learning Machine (ELM); Support Vector Machine (SVM) and K-Nearest Neighbours (KNN) for the obtained feature sets. Our developed models are tested on a publicly available MCI EEG database and the robustness of our models is evaluated by using a 10-fold cross validation method. The results show that the proposed ELM based method achieves the highest classification accuracy (98.78%) with lower execution time (0.281 seconds) and also outperforms the existing methods. The experimental results suggest that our proposed framework could provide a robust biomarker for efficient detection of MCI patients.

On the automatic parameter selection for permutation entropy

Permutation Entropy (PE) is a cost effective tool for summarizing the complexity of a time series. It has been used in many applications including damage detection, disease forecasting, detection of dynamical changes, and financial volatility analysis. However, to successfully use PE, an accurate selection of two parameters is needed: the permutation dimension n and embedding delay τ. These parameters are often suggested by experts based on a heuristic or by a trial and error approach. Both of these methods can be time-consuming and lead to inaccurate results. In this work, we investigate multiple schemes for automatically selecting these parameters with only the corresponding time series as the input. Specifically, we develop a frequency-domain approach based on the least median of squares and the Fourier spectrum, as well as extend two existing methods: Permutation Auto-Mutual Information Function and Multi-scale Permutation Entropy (MPE) for determining τ. We then compare our methods as well as current methods in the literature for obtaining both τ and n against expert-suggested values in published works. We show that the success of any method in automatically generating the correct PE parameters depends on the category of the studied system. Specifically, for the delay parameter τ, we show that our frequency approach provides accurate suggestions for periodic systems, nonlinear difference equations, and electrocardiogram/electroencephalogram data, while the mutual information function computed using adaptive partitions provides the most accurate results for chaotic differential equations. For the permutation dimension n, both False Nearest Neighbors and MPE provide accurate values for n for most of the systems with a value of n=5 being suitable in most cases.

Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

The development of new measures and algorithms to quantify the entropy or related concepts of a data series is a continuous effort that has brought many innovations in this regard in recent years. The ultimate goal is usually to find new methods with a higher discriminating power, more efficient, more robust to noise and artifacts, less dependent on parameters or configurations, or any other possibly desirable feature. Among all these methods, Permutation Entropy (PE) is a complexity estimator for a time series that stands out due to its many strengths, with very few weaknesses. One of these weaknesses is the PE’s disregarding of time series amplitude information. Some PE algorithm modifications have been proposed in order to introduce such information into the calculations. We propose in this paper a new method, Slope Entropy (SlopEn), that also addresses this flaw but in a different way, keeping the symbolic representation of subsequences using a novel encoding method based on the slope generated by two consecutive data samples. By means of a thorough and extensive set of comparative experiments with PE and Sample Entropy (SampEn), we demonstrate that SlopEn is a very promising method with clearly a better time series classification performance than those previous methods.

Spillover effects of Great Recession on Hong-Kong's Real Estate Market: An analysis based on Causality Plane and Tsallis Curves of Complexity-Entropy

This paper investigates the impact of the sub-prime loan crisis on the Real Estate Market of Hong-Kong. Based on permutation entropy, complexity-entropy causality plane and Tsallis complexity-entropy curve, we characterize the complexity of the housing indices-both in terms of size and region-and distinguish the level of informational efficiency. By calculating the quantifiers we report that most indices exhibit a behavior equivalent to a persistent stochastic dynamics with Hurst exponents between 0.5 and 0.7. The outbreak of the crisis had changed the dynamical structure of the indices decreasing the level of randomness and increasing considerably their regularity and predictability. Only the index of the Kowloon area seems not impacted by the crisis, exhibiting higher levels of informational efficiency. The results are robust based on the utilization of two different entropy definitions: The Shannon and Tsallis-q entropy. Lastly, with the temporal evolution of the indices, we identify periods where the underlying dynamical structure of the market was impacted by certain events like the SARS epidemic and the imposition of Special Stamp Duty on housing.

Use of Multiple EEG Features and Artificial Neural Network to Monitor the Depth of Anesthesia

The electroencephalogram (EEG) can reflect brain activity and contains abundant information of different anesthetic states of the brain. It has been widely used for monitoring depth of anesthesia (DoA). In this study, we propose a method that combines multiple EEG-based features with artificial neural network (ANN) to assess the DoA. Multiple EEG-based features can express the states of the brain more comprehensively during anesthesia. First, four parameters including permutation entropy, 95% spectral edge frequency, BetaRatio and SynchFastSlow were extracted from the EEG signal. Then, the four parameters were set as the inputs to an ANN which used bispectral index (BIS) as the reference output. 16 patient datasets during propofol anesthesia were used to evaluate this method. The results indicated that the accuracies of detecting each state were 86.4% (awake), 73.6% (light anesthesia), 84.4% (general anesthesia), and 14% (deep anesthesia). The correlation coefficient between BIS and the index of this method was 0.892 (p<0.001). The results showed that the proposed method could well distinguish between awake and other anesthesia states. This method is promising and feasible for a monitoring system to assess the DoA.

Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ. Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ, only general recommendations such as N>>m!, τ=1, or m=3,…,7. This paper deals specifically with the study of the practical implications of N>>m!, since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N>>m! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

Measuring Alterations of Spontaneous EEG Neural Coupling in Alzheimer's Disease and Mild Cognitive Impairment by Means of Cross-Entropy Metrics

Alzheimer's Disease (AD) represents the most prevalent form of dementia and is considered a major health problem due to its high prevalence and its economic costs. An accurate characterization of the underlying neural dynamics in AD is crucial in order to adopt effective treatments. In this regard, mild cognitive impairment (MCI) is an important clinical entity, since it is a risk-state for developing dementia. In the present study, coupling patterns of 111 resting-state electroencephalography (EEG) recordings were analyzed. Specifically, we computed Cross-Approximate Entropy (Cross-ApEn) and Cross-Sample Entropy (Cross-SampEn) of 37 patients with dementia due to AD, 37 subjects with MCI, and 37 healthy control (HC) subjects. Our results showed that Cross-SampEn outperformed Cross-ApEn, revealing higher number of significant connections among the three groups (Kruskal-Wallis test, FDR-corrected p-values < 0.05). AD patients exhibited statistically significant lower similarity values at θ and β1 frequency bands compared to HC. MCI is also characterized by a global decrease of similarity in all bands, being only significant at β1. These differences shows that β band might play a significant role in the identification of early stages of AD. Our results suggest that Cross-SampEn could increase the insight into brain dynamics at different AD stages. Consequently, it may contribute to develop early AD biomarkers, potentially useful as diagnostic information.

Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm

BACKGROUND AND OBJECTIVES

The adoption in clinical practice of electronic portable blood or interstitial glucose monitors has enabled the collection, storage, and sharing of massive amounts of glucose level readings. This availability of data opened the door to the application of a multitude of mathematical methods to extract clinical information not discernible with conventional visual inspection. The objective of this study is to assess the capability of Permutation Entropy (PE) to find differences between glucose records of healthy and potentially diabetic subjects.

METHODS

PE is a mathematical method based on the relative frequency analysis of ordinal patterns in time series that has gained a lot of attention in the last years due to its simplicity, robustness, and performance. We study in this paper the applicability of this method to glucose records of subjects at risk of diabetes in order to assess the predictability value of this metric in this context.

RESULTS

PE, along with some of its derivatives, was able to find significant differences between diabetic and non-diabetic patients from records acquired up to 3 years before the diagnosis. The quantitative results for PE were 3.5878 ± 0.3916 for the nondiabetic class, and 3.1564 ± 0.4166 for the diabetic class. With a classification accuracy higher than 70%, and by means of a Cox regression model, PE demonstrated that it is a very promising candidate as a risk stratification tool for continuous glucose monitoring.

CONCLUSION

PE can be considered as a prospective tool for the early diagnosis of the glucoregulatory system.

A Comparison of Multiscale Permutation Entropy Measures in On-Line Depth of Anesthesia Monitoring

OBJECTIVE

Multiscale permutation entropy (MSPE) is becoming an interesting tool to explore neurophysiological mechanisms in recent years. In this study, six MSPE measures were proposed for on-line depth of anesthesia (DoA) monitoring to quantify the anesthetic effect on the real-time EEG recordings. The performance of these measures in describing the transient characters of simulated neural populations and clinical anesthesia EEG were evaluated and compared.

METHODS

Six MSPE algorithms-derived from Shannon permutation entropy (SPE), Renyi permutation entropy (RPE) and Tsallis permutation entropy (TPE) combined with the decomposition procedures of coarse-graining (CG) method and moving average (MA) analysis-were studied. A thalamo-cortical neural mass model (TCNMM) was used to generate noise-free EEG under anesthesia to quantitatively assess the robustness of each MSPE measure against noise. Then, the clinical anesthesia EEG recordings from 20 patients were analyzed with these measures. To validate their effectiveness, the ability of six measures were compared in terms of tracking the dynamical changes in EEG data and the performance in state discrimination. The Pearson correlation coefficient (R) was used to assess the relationship among MSPE measures.

RESULTS

CG-based MSPEs failed in on-line DoA monitoring at multiscale analysis. In on-line EEG analysis, the MA-based MSPE measures at 5 decomposed scales could track the transient changes of EEG recordings and statistically distinguish the awake state, unconsciousness and recovery of consciousness (RoC) state significantly. Compared to single-scale SPE and RPE, MSPEs had better anti-noise ability and MA-RPE at scale 5 performed best in this aspect. MA-TPE outperformed other measures with faster tracking speed of the loss of unconsciousness.

CONCLUSIONS

MA-based multiscale permutation entropies have the potential for on-line anesthesia EEG analysis with its simple computation and sensitivity to drug effect changes. CG-based multiscale permutation entropies may fail to describe the characteristics of EEG at high decomposition scales.

Pupil Size in Relation to Cortical States during Isoflurane Anesthesia

In neuronal recording studies on anesthetized animals, reliable measures for the transitional moment of consciousness are frequently required. Previous findings suggest that pupil fluctuations reflect the neuronal states during quiet wakefulness, whose correlation was unknown for the anesthetized condition. Here, we investigated the pupillary changes under isoflurane anesthesia simultaneously with the electroencephalogram (EEG) and electromyogram (EMG). The pupil was tracked by using a region-based active contour model. The dose was given to the animal in a stepwise increasing mode (simulating induction of anesthesia) or in a stepwise decreasing mode (simulating emergence of anesthesia). We found that the quickly widening pupil action (mydriasis) characterizes the transitional state in anesthesia. Mydriasis occurred only in the light dose in the emergence phase, and the events were accompanied by an increase of burst activity in the EEG followed by EMG activity in 47% of the mydriasis events. Our findings suggest that recording such pupil changes may offer a noncontact monitoring tool for indexing the transitional state of the brain, particularly when a lower threshold dose is applied.

Analysis of EEG signals regularity in adults during video game play in 2D and 3D

Video games have long been part of the entertainment industry. Nonetheless, it is not well known how video games can affect us with the advancement of 3D technology. The purpose of this study is to investigate the EEG signals regularity when playing video games in 2D and 3D modes. A total of 29 healthy subjects (24 male, 5 female) with mean age of 21.79 (1.63) years participated. Subjects were asked to play a car racing video game in three different modes (2D, 3D passive and 3D active). In 3D passive mode, subjects needed to wear a passive polarized glasses (cinema type) while for 3D active, an active shutter glasses was used. Scalp EEG data was recorded during game play using 19-channel EEG machine and linked ear was used as reference. After data were pre-processed, the signal irregularity for all conditions was computed. Two parameters were used to measure signal complexity for time series data: i) Hjorth-Complexity and ii) Composite Permutation Entropy Index (CPEI). Based on these two parameters, our results showed that the complexity level increased from eyes closed to eyes open condition; and further increased in the case of 3D as compared to 2D game play.

EEG entropy measures in anesthesia

HIGHLIGHTS

► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression.

OBJECTIVE

Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents.

METHODS

Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared.

RESULTS

All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R (2)) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation efficiency compared with MDFA.

CONCLUSION

Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure. Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.

Characterizing system dynamics with a weighted and directed network constructed from time series data

In this work, we propose a novel method to transform a time series into a weighted and directed network. For a given time series, we first generate a set of segments via a sliding window, and then use a doubly symbolic scheme to characterize every windowed segment by combining absolute amplitude information with an ordinal pattern characterization. Based on this construction, a network can be directly constructed from the given time series: segments corresponding to different symbol-pairs are mapped to network nodes and the temporal succession between nodes is represented by directed links. With this conversion, dynamics underlying the time series has been encoded into the network structure. We illustrate the potential of our networks with a well-studied dynamical model as a benchmark example. Results show that network measures for characterizing global properties can detect the dynamical transitions in the underlying system. Moreover, we employ a random walk algorithm to sample loops in our networks, and find that time series with different dynamics exhibits distinct cycle structure. That is, the relative prevalence of loops with different lengths can be used to identify the underlying dynamics.